Problem: Which of the following numbers is a factor of 72? ${7,9,10,13,14}$
By definition, a factor of a number will divide evenly into that number. We can start by dividing $72$ by each of our answer choices. $72 \div 7 = 10\text{ R }2$ $72 \div 9 = 8$ $72 \div 10 = 7\text{ R }2$ $72 \div 13 = 5\text{ R }7$ $72 \div 14 = 5\text{ R }2$ The only answer choice that divides into $72$ with no remainder is $9$ $ 8$ $9$ $72$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $72$ $72 = 2\times2\times2\times3\times3 9 = 3\times3$ Therefore the only factor of $72$ out of our choices is $9$. We can say that $72$ is divisible by $9$.